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  <title>Simple 2D Flexible Spacecraft</title>
                                         
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<div align="center">      <img src="Simple2DFlexSC.GIF" alt="Title"
 width="544" height="64">
       
<div align="left"><b><u>Simulation Control</u></b><br>
 <br>
     <b>time step</b>:         Time step for the numerical integration routine<br>
     <b>time</b>:                Duration of the simulation periond in seconds<br>
    <b><u><br>
 </u></b>   </div>
         
<div align="left"><b><u>Description<br>
 </u></b><br>
    A flexible spacecraft is modeled as a central rigid body with two massless
  beams<br>
     attachd symmetrically to the side of the central body. Each beam has 
a  <br>
     concentrated mass at the tip. The flexibility comes from the flexural
 rigidity  EI of <br>
     the beams.<br>
     <img src="Flexible202D.GIF"
 alt="2D Flexible Spacecraft Illustration" width="540" height="424">
    <br>
   <b><u>Inputs<br>
 </u></b><br>
   <b>J</b>:                &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; Moment of inertia<br>
   <b>m</b>:                &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; Tip mass<br>
   <b>a</b>:                &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; Distance as indicated in
the illustration above  (m)<br>
   <b>L</b>:                &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; Length of the beam (m)<br>
   <b>EI</b>:               &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; Flexural rigidity of the
beam (N m2) <br>
   <b><u><small><br>
   </small>Initial Condition<br>
 </u></b><br>
   <b>Alpha</b>:           &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; Spacecraft angular position  <br>
   <b>u1</b>:               &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; Position of the first mass<br>
   <b>u2</b>:               &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; Position of the second mass<br>
   <b>AlphaDot</b>:      &#160;&#160;&#160; &#160;&#160; Spacecraft angular velocity <br>
   <b>u1Dot</b>:          &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; Velocity of the first mass<br>
   <b>u2Dot</b>:          &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; Velocity of the second mass<br>
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 <img src="2DFlexInputOutput.GIF" alt="Input and Output" width="606"
 height="745">
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